Score : $600$ points

Problem Statement

Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, \cdots, N$, and the $i$-th edge connects Vertices $a_i$ and $b_i$. Also given is a sequence of positive integers: $c_1, c_2, \cdots, c_N$.

Convert this graph into a directed graph that satisfies the condition below, that is, for each $i$, delete the undirected edge $(a_i, b_i)$ and add one of the two direted edges $a_i \to b_i$ and $b_i \to a_i$.

• For every $i = 1, 2, \cdots, N$, there are exactly $c_i$ vertices reachable from Vertex $i$ (by traversing some number of directed edges), including Vertex $i$ itself.

In this problem, it is guaranteed that the given input always has a solution.

Constraints

• $1 \leq N \leq 100$
• $0 \leq M \leq \frac{N(N - 1)}{2}$
• $1 \leq a_i, b_i \leq N$
• The given graph has no self-loops and no multi-edges.
• $1 \leq c_i \leq N$
• There always exists a valid solution.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$a_1$ $b_1$

$:$

$a_M$ $b_M$

$c_1$ $c_2$ $...$ $c_N$

Output

Print $M$ lines.

To add the edge $a_i \to b_i$ for the $i$-th edge, print -> in the $i$-th line; to add the edge $b_i \to a_i$ for the $i$-th edge, print <-.

If there are multiple solutions, any of them will be accepted.

3 3
1 2
2 3
3 1
3 3 3

->
->
->

In a cycle of length $3$, you can reach every vertex from any vertex.

3 2
1 2
2 3
1 2 3

<-
<-

6 3
1 2
4 3
5 6
1 2 1 2 2 1

<-
->
->

The graph may be disconnected.